On 25 October 2011, after another game on the bench, Cuenca made his La Liga debut, playing the full 90 minutes and being booked in a 1–0 away win against Granada CF.[8] Four days later, again as a starter, he scored in a 5–0 home success over RCD Mallorca, assisted by Adriano.[9]

On 3 December 2011 Cuenca netted his second league goal, playing the entire 5–0 home routing of Levante UD.[10] On 31 January 2012 he signed a contract extension with the Blaugrana, keeping him at the club until June 2015,[11] and also switched permanently to the first team, being assigned jersey number 23.

Cuenca spent the first half of the 2012–13 season nursing a knee injury.[12][13] On 31 January 2013, he was loaned to Eredivisie side AFC Ajax until the end of the campaign.[14] He was given the number 11 shirt, which was previously worn by Lorenzo Ebecilio; that jersey, however, was reserved for league and Dutch Cup matches, while he wore number 28 in the team run in the UEFA Europa League, as Ebecilio had already made continental appearances with the club wearing the former number during the season.[15]

Cuenca made his debut for his new team 10 February 2013, against Roda JC Kerkrade at the Amsterdam Arena, assisting Daley Blind in his first ever goal for Ajax as the match ended in a 1–1 draw.[16] However, in March, he suffered another knee injury, being sidelined for a further four months;[17] he underwent surgery in early June,[18] returning to training in October.[19]

On 10 July 2014 Cuenca and Barcelona reached an agreement to rescind the player's contract, due to expire in June 2015, due to technical reasons.[20] Late in the same day, he signed a one-year deal with fellow league team Deportivo de La Coruña.[21]